Travelling to US with a criminal record in the UK

Hi everyone Ive been reading through a few forums and I still can't get the answer what im looking for, can someone help me.

Basically around a 2 months ago, I received a simple caution, for returning to the same area, once the police told me not to, It was a drunken night. I know the caution is under the rehabilation act.

I'm 18 and a British national, I also have an American visa from previous visits which expires in 10 years, on my other passport because i have a dual nationality and only recent became British.

and I am planning to travel to the U.S. in late July, which my dad lives there and I am going to visit for a few weeks and I am wondering if I need to confess anything, because the incident was really nothing serious, if anything a laugh. Because i didn't get arrested or anything, but I want to double check because I don't want any trouble.

HelloI have an appointment at the embassy this week in order to ask for a visa Is there any chance that the us embassy contact my parents ?I am 22 but still a student. Since I am dependent on them financially speaking I am worried that they call them or ask me to provide some papers about their situation.As you can imagine they dont know about my caution and hope this will never reach their earsthanks for your help

Thank you for your replies.My caution is for possession of class A, back in 2013This is something I deeply regret and hopefully my parents don't know about it. If there's any chance the Embassy call them Im gonna drop out my visa application and try again in a few years when I will be financially independent